Connecting DG and DF

∫D, g and f are the midpoint of each side.

∴DG parallel equals half AC, DF parallel equals half AB,

∴ Angle DFE= = Angle A = Angle GDF, Angle BGD= = Angle A, quadrilateral AGDF is a parallelogram.

The degrees of arc AD, arc DE and arc GF are all 72 degrees, so the sum of the degrees of arc HG and arc EF is 144 degrees.

And ∵GF is parallel and equal to half of BC,

∴ Arc Hg = Arc EF, all degrees are 72 degrees,

∴ arc de = arc ef = arc fg = arc GH = arc HD,

A pentagon is defined as a regular pentagon.

This is the result of my long-term thinking. I hope the landlord will adopt it. Thank you.